Math 3 Unit 3 Review

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are constants and n is a non-negative integer.

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What does it mean for a polynomial to have zeros?

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Zeros of a polynomial are the values of x for which the polynomial evaluates to zero. They represent the x-intercepts of the graph of the polynomial.

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How do you find the remainder when dividing a polynomial by a linear factor?

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You can use the Remainder Theorem, which states that the remainder of the division of a polynomial p(x) by (x - c) is p(c).

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c). It involves using the coefficients of the polynomial and performing a series of multiplications and additions.

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What is the significance of the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. It determines the polynomial's end behavior and the maximum number of roots it can have.

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What is a factor of a polynomial?

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A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder. If (x - c) is a factor of p(x), then p(c) = 0.

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How do you determine if (x - c) is a factor of a polynomial?

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You can use the Factor Theorem, which states that (x - c) is a factor of p(x) if and only if p(c) = 0.

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What is the process of polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of equal or lower degree. It involves dividing the leading terms, multiplying, and subtracting until the remainder is of lower degree.

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What is the relationship between the zeros and the factors of a polynomial?

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The zeros of a polynomial correspond to the values of x that make the polynomial equal to zero, and each zero (c) corresponds to a factor of the form (x - c).

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What is the multiplicity of a zero?

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The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial. A zero with an odd multiplicity will cross the x-axis, while one with an even multiplicity will touch the x-axis.